0:00:11.170,0:00:15.140 This is the pangolin of Eric Joisel.[br]It is an origami, 0:00:15.140,0:00:18.850 it is folded by only one esagonal[br]sheet of paper, without any cut. 0:00:18.850,0:00:21.410 Origami's rules are easy: 0:00:21.410,0:00:25.760 (Applause) 0:00:30.140,0:00:35.610 you take a sheet of paper and fold it,[br]you don't use any scissors or glue. 0:00:36.800,0:00:40.890 Origami is an art - and it takes[br]a bit of courage to say it - 0:00:40.890,0:00:44.039 because almost all[br]think that origami is simply... 0:00:44.039,0:00:46.839 a child's play. 0:00:46.839,0:00:49.000 I will try to change your mind. 0:00:49.000,0:00:51.359 Today origami is this: 0:00:52.479,0:00:57.629 every model has its author,[br]this is a horse made by Roman Diaz... 0:00:57.629,0:01:02.250 who is a veterinary capable to[br]capture the essence of animals. 0:01:02.250,0:01:06.470 Instead Robert Lang[br]is one of the origami's theorists. 0:01:06.470,0:01:10.010 Among other things,[br]he formulated a theory... 0:01:10.010,0:01:14.040 about how to design complex origami,[br]of which I will just tell you something. 0:01:15.200,0:01:18.659 This is a model of mine,[br]a three-dimensional pram. 0:01:20.669,0:01:26.630 Satoshi Kamiya is known for creating[br]very complex models like this wasp, 0:01:26.630,0:01:32.380 while Giang Dinh[br]made simplicity his magic bullet: 0:01:32.380,0:01:34.120 he works with wet cardboard, 0:01:34.120,0:01:37.789 he sprinkles it[br]and he can obtain these plastic figures. 0:01:39.169,0:01:45.270 Eric Joisel is an other author,[br]the pangolin's author too, 0:01:45.270,0:01:48.690 and he is a master[br]in creating also human figures 0:01:48.690,0:01:52.350 and using the volume of the paper 0:01:52.350,0:01:56.950 to create effects like, for example,[br]Harlequin's legs. 0:01:58.040,0:02:02.310 How have we reached this point? 0:02:02.630,0:02:07.429 Let's start from the simpliest thing:[br]the square base. 0:02:07.969,0:02:13.830 It is a paper square. First you fold[br]the medians, then the diagonals, 0:02:13.830,0:02:19.709 close it and you obtain this figure:[br]it is a square base and it has 4 flaps. 0:02:19.709,0:02:23.720 No surprises, it comes from a square:[br]4 sides, 4 angles, 4 flaps. 0:02:23.720,0:02:26.000 Folding a model by John Montroll, 0:02:26.000,0:02:29.959 at a certain point,[br]you get your hands on this stuff, 0:02:29.959,0:02:33.819 which seems a square base,[br]but has 5 flaps instead of 4. 0:02:33.819,0:02:36.290 So you ask yourself, 0:02:36.290,0:02:39.870 "But how, I started from a square:[br]where does the fifth flap come from?" 0:02:39.870,0:02:42.510 The trick to understand this,[br] 0:02:42.510,0:02:46.290 to understand how it works,[br]is to reopen the sheet. 0:02:46.290,0:02:50.800 So you reopen the sheet[br]and you will see that the author... 0:02:50.800,0:02:54.209 didn't do nothing but drawing[br]a pentagon inside the square... 0:02:54.209,0:02:56.330 and hiding all the exceeding paper. 0:02:56.330,0:02:59.269 So the message here is, 0:02:59.269,0:03:04.119 "If you want to understand[br]how it works, reopen the model." 0:03:06.899,0:03:13.950 This is one of the scorpions[br]made by Robert Lang... 0:03:13.950,0:03:14.989 it has a lot of tips. 0:03:14.989,0:03:19.900 To understand how this runs,[br]it has to know how an umbrella works. 0:03:19.900,0:03:23.950 So imagine:[br]a closed umbrella is the folded end, 0:03:23.950,0:03:27.860 an open umbrella is the paper[br]which is needed to obtain that end. 0:03:29.290,0:03:33.019 A bigger umbrella[br]will give a longer end. 0:03:34.219,0:03:37.989 This is the same model,[br]the same scorpion but reopened. 0:03:39.709,0:03:43.950 It has been folded[br]and then reopened, 0:03:43.950,0:03:46.900 marking the position[br]of its different ends. 0:03:46.900,0:03:49.049 Every point is a circle, an umbrella: 0:03:49.049,0:03:52.180 that big umbrella, the blue one,[br]is for the tail, 0:03:52.180,0:03:56.530 the red ones are the paws,[br]the green ones are the claws. 0:03:57.460,0:03:59.239 Now we go back to our presentation. 0:04:03.409,0:04:05.420 This is the figure you have just seen, 0:04:05.420,0:04:07.489 and this map of the folds... 0:04:07.489,0:04:10.260 is called technically ‘crease pattern’. 0:04:10.260,0:04:16.130 This is the Lang original version,[br]where you can see all the work folds. 0:04:16.130,0:04:20.320 Therefore the problem of projecting[br]a complex origami turns into... 0:04:20.320,0:04:26.050 the mathematic problem of having[br]the circles on the plane opportunely. 0:04:26.050,0:04:31.570 It's not only circles, you can see[br]that there are also some figures, 0:04:31.570,0:04:35.380 they are lightly out of sorts but[br]they would show some streams... 0:04:35.380,0:04:38.850 which divide the points and can give[br]a topology to the model. 0:04:40.870,0:04:45.870 Let's take a step back in time:[br]there is as such geometry of origami, 0:04:45.870,0:04:47.630 made of axioms and theorems. 0:04:49.090,0:04:53.160 It is a more powerful geometry[br]than the ’ruler and compass‘ one, 0:04:53.160,0:04:56.650 meaning that all the workable[br]constructions with ruler and compass... 0:04:56.650,0:04:58.350 are also workable with origami, 0:04:58.350,0:05:03.320 but origami can do other ones, such[br]dividing an angle into three equal parts. 0:05:04.560,0:05:06.720 A small example of origami geometry: 0:05:06.720,0:05:10.370 we start from this square,[br]we make these folds... 0:05:10.370,0:05:12.500 and what we obtain[br]is this figure here. 0:05:12.500,0:05:14.330 They are only three folds, 0:05:14.330,0:05:20.070 but you can glimpse a big triangle,[br]which I state it is equilateral. 0:05:20.070,0:05:23.600 It is equilateral because its sides... 0:05:23.600,0:05:26.800 are three of the square's sides,[br]so all they are equals, ok? 0:05:26.800,0:05:30.690 And if it is an equilateral triangle[br]these are exactly 60 degrees, 0:05:30.690,0:05:35.800 therefore I can find very easily[br]60 degrees from a square. 0:05:35.800,0:05:41.200 An other example concerns... 0:05:41.200,0:05:44.200 the division of a sheet in equal parts. 0:05:44.200,0:05:47.210 As you can see,[br]the points on the diagonal are six... 0:05:47.210,0:05:50.160 and so they divide that segment[br]into five equal parts. 0:05:50.790,0:05:53.440 On the other diagonal[br]the division is in thirds, 0:05:53.440,0:05:57.070 therefore, through very few folds,[br]which are that ones highlighted here, 0:05:57.070,0:06:00.190 I can obtain[br]a division in fifths and thirds. 0:06:00.190,0:06:03.900 Why do I need this for,[br]maybe we will discover it later. 0:06:03.900,0:06:07.780 In origami, one of the best moves[br]is the twist. 0:06:07.780,0:06:12.780 The twist is built[br]on a central polygon 0:06:12.780,0:06:15.780 going around and some parallel folds... 0:06:15.780,0:06:18.340 which spread out two by two[br]from the polygon. 0:06:18.340,0:06:20.650 It is so called because[br]when you make this fold, 0:06:20.650,0:06:23.220 the central polygon actually[br]makes a rotation. 0:06:23.220,0:06:24.750 What is twist used for? 0:06:24.750,0:06:28.050 The twist it is for creating[br]some roses like this. 0:06:28.050,0:06:32.640 This one is built on a pentagonal twist, 0:06:32.640,0:06:35.640 it is by Naomiki Sato. 0:06:35.640,0:06:39.650 Or it is for creating[br]tessellations, like these here. 0:06:39.650,0:06:41.910 Especially look that in the middle, 0:06:41.910,0:06:44.530 which soon you will see in a new light. 0:06:45.580,0:06:48.240 Tessellations can also be very complex, 0:06:48.240,0:06:51.240 like this made by Alessandro Beber: 0:06:51.240,0:06:55.990 this has some twists[br]with 12, 3, 4 and 6 sides. 0:06:57.990,0:07:01.090 Twists are also used in technology: 0:07:01.090,0:07:03.610 here the question[br]is that of a solar panel... 0:07:03.610,0:07:05.930 which has to be locked up[br]in a rocket... 0:07:05.930,0:07:10.490 or a shuttle, to be thrown[br]and, when it is in space, 0:07:10.490,0:07:14.540 it has to be opened[br]with minimum effort and damage. 0:07:14.540,0:07:19.630 This is the series of moves to be done. 0:07:22.670,0:07:23.670 It is this. 0:07:24.750,0:07:27.560 This is how it is thrown, then, 0:07:27.560,0:07:32.150 once it is high, it opens. 0:07:32.810,0:07:35.810 (Applause) 0:07:40.080,0:07:43.110 This is a twist... 0:07:43.110,0:07:46.890 and this is a tessellation of a twist,[br]it is the former beehive. 0:07:46.890,0:07:50.680 So, as you can see,[br]each hexagonal stuff... 0:07:50.680,0:07:52.370 can be opened. 0:07:56.020,0:08:00.190 Therefore[br]these are related to each other. 0:08:00.190,0:08:04.970 I go mad for motion origami,[br]which are these I'm showing you. 0:08:04.970,0:08:07.400 This is a fractal: 0:08:07.400,0:08:13.440 it means that I have[br]a row made of 12 external petals, 0:08:13.440,0:08:15.310 a bit smaller one, 0:08:15.310,0:08:17.870 which have the same shape[br]but different dimension. 0:08:17.870,0:08:21.050 And this is a single paper sheet. 0:08:21.500,0:08:23.670 (Applause) 0:08:23.670,0:08:29.920 The surprising thing[br]is not only its opening, 0:08:31.020,0:08:35.299 but its closing, because paper remembers. 0:08:35.299,0:08:38.299 (Applause) 0:08:38.689,0:08:41.950 I want to amaze you again[br]with a pair of motion models: 0:08:42.630,0:08:47.750 this is called flexicube, 0:08:47.750,0:08:50.670 it is made from a single paper strip... 0:08:50.670,0:08:52.480 which composes 8 little hinged cubes, 0:08:52.480,0:08:54.719 in order to have this continuous movement. 0:08:54.719,0:08:58.360 Instead this is its father:[br]the double star flexicube, 0:08:58.360,0:08:59.970 a model by Dave Brill. 0:08:59.970,0:09:03.860 Although it is a flexicube also,[br]it is the only model not made of... 0:09:03.860,0:09:07.600 a single paper sheet,[br]there are 64 fitted modules. 0:09:07.600,0:09:10.530 It can go round also,[br]but at a certain point I can stop, 0:09:12.000,0:09:16.610 I can open the trunk[br]and pull out the first star. 0:09:17.840,0:09:23.290 But it is a double star felxicube, 0:09:23.290,0:09:26.290 because there are two stars. 0:09:26.290,0:09:29.290 (Applause) 0:09:29.820,0:09:34.459 Here I let you imagine[br]how much geometry is inside here, 0:09:34.459,0:09:38.139 but this is half cube and this an other[br]half cube: they are pulled together. 0:09:38.139,0:09:43.379 But also this is half cube:[br]this is half cube, the star, 0:09:43.379,0:09:46.250 and if I turn it,[br]it will become a box for stars, 0:09:46.250,0:09:50.060 that is a box which exactly has[br]the space to contain a star inside. 0:09:53.720,0:09:56.720 (Applause) 0:09:56.740,0:09:59.050 Why would anyone make origami? 0:09:59.050,0:10:01.660 There are a lot of reasons. 0:10:01.660,0:10:05.930 Origami instigates manual skills,[br]fantasy and creativity, 0:10:05.930,0:10:08.170 makes children like Maths. 0:10:08.170,0:10:09.799 The reason why I fold origami... 0:10:09.799,0:10:14.610 is because it is nice: it is magic,[br]the magic of transformation really. 0:10:16.130,0:10:20.310 The ‘Center for diffusion of origami’[br]is a no-profit association... 0:10:20.310,0:10:25.529 which gathers all Italian origamists[br]and also organise meetings. 0:10:25.529,0:10:27.970 The meetings about origami[br]are hotbeds of ideas... 0:10:27.970,0:10:30.970 where everyone brings his own models,[br]shows them, 0:10:30.970,0:10:33.860 explains them[br]and makes them fold by others. 0:10:33.860,0:10:36.120 In this way there is a fusion of ideas... 0:10:36.120,0:10:40.649 that has also brought to meetings[br]about origami and teaching. 0:10:40.649,0:10:42.389 Now we are organizing... 0:10:42.389,0:10:44.499 the third meeting for next April. 0:10:44.499,0:10:47.769 It will be a great chance,[br]for teachers and instructors... 0:10:47.769,0:10:49.399 who wants to use origami... 0:10:49.399,0:10:55.100 for their job, to get in touch[br]with different opportunities. 0:10:56.860,0:11:01.819 I wanted to finish with Zsebe's bear,[br]showing how it folds, 0:11:01.819,0:11:04.609 but I don't know if I still have time... 0:11:05.439,0:11:07.849 Yes? Do I still have time? 0:11:07.849,0:11:09.350 Claudio Ruatti: Take a minute! 0:11:09.350,0:11:14.089 RG: I will take a minute then, here it is! 0:11:14.089,0:11:20.350 I have already folded something[br]because otherwise I could not do it. 0:11:20.350,0:11:23.619 Here one can already infer[br]a little structure: 0:11:23.619,0:11:28.100 this will become a bear,[br]with head and tail. 0:11:28.100,0:11:33.829 From the head one can obtain[br]the ears in some way, 0:11:33.829,0:11:38.189 then the great thing[br]is the way you shape the head. 0:11:38.189,0:11:42.939 Now here we need to zoom in[br]really to this part. 0:11:42.939,0:11:46.470 So, first you fold up,[br]now I have exactly a rhombus. 0:11:49.590,0:11:53.540 I fold up its face,[br]then I squash from the inside... 0:11:53.540,0:11:56.699 and I close the top part,[br]which will become the bear's hump. 0:11:56.699,0:12:00.610 It is taking the shape of a bear,[br]you can see its face, 0:12:00.610,0:12:05.209 but now the basic move:[br]it is an upstream fold here, 0:12:05.209,0:12:07.479 followed by a downstream fold[br]placed right down, 0:12:13.439,0:12:16.709 which make the bear's face pop up. 0:12:16.709,0:12:19.800 Sorry, it has come off a bit like that. 0:12:19.800,0:12:22.309 (Applause) 0:12:24.439,0:12:28.389 This is how the model should be. 0:12:29.609,0:12:33.569 I have finished my presentation,[br]more or less. 0:12:33.569,0:12:36.420 This is a model created for this occasion: 0:12:37.990,0:12:41.499 it is a model which basically has a cut. 0:12:41.499,0:12:44.259 What happens is that... 0:12:44.259,0:12:48.659 one has a sheet of paper and folds it 0:12:48.659,0:12:51.189 - as you can see,[br]the TED logo has been drawn. 0:12:55.009,0:12:57.930 What happens is that if one just cut it, 0:12:57.930,0:13:04.129 which you should not do with origami,[br]but if one makes a single cut here, 0:13:04.559,0:13:09.639 he will separate the three letters[br]and obtain the figure you were seeing. 0:13:10.199,0:13:13.199 (Applause) 0:13:13.199,0:13:14.209 Thank you.